Decimals
How to Divide Decimals
To divide decimals, move the decimal point in the divisor to the right until it is a whole number, move the point in the dividend the same number of places, and divide as usual. So 4.5 ÷ 0.3 becomes 45 ÷ 3 = 15. This guide covers dividing decimals by whole numbers, by other decimals and into whole numbers, plus repeating answers, rounding and checking.
How to divide decimals
To divide decimals, make the divisor (the number you are dividing by) a whole number first. Move its decimal point to the right until it is a whole number, move the decimal point in the dividend the same number of places, and then divide as usual. The decimal point in the answer goes straight above the decimal point in the dividend.
- Look at the divisor. If it is already a whole number, skip to step 3.
- Move both decimal points. Shift the divisor’s point right until it is a whole number. Shift the dividend’s point right by the same number of places, adding zeros if you run out of digits.
- Divide. Use long division exactly as you would with whole numbers.
- Place the point. Put the decimal point in the answer directly above the decimal point in the dividend.
Example: 4.5 ÷ 0.3
The divisor 0.3 has one decimal place. Move both points one place right.
The answer, 15, is bigger than 4.5. That is correct: there are fifteen 0.3s in 4.5.
The long division calculator shows every step of the division once the divisor is whole, and the division calculator gives a quick answer to check against.
Why moving the decimal point works
Moving both decimal points one place to the right multiplies both numbers by 10. A division is a fraction, and multiplying the top and bottom of a fraction by the same number does not change its value.
It is the same reason equivalent fractions such as 1/2 and 5/10 are equal. You can see it with money as well: how many 30-cent coins make $4.50 is the same question as how many 30s make 450, since both are counted in cents. The answer is 15 either way.
What you cannot do is move only one of the two points. That multiplies just the top or just the bottom by 10, and the answer comes out ten times too large or too small.
Dividing a decimal by a whole number
When the divisor is already a whole number, there is nothing to move. Divide as normal and carry the decimal point straight up into the answer.
Example: 9.36 ÷ 4
9.36 ÷ 4 = 2.34. Check: 2.34 × 4 = 9.36.
A simpler one: 7.5 ÷ 3 = 2.5. Three goes into 7 twice with 1 left, the point goes up, and three goes into 15 five times.
When the dividend runs out of digits
If there is still a remainder after the last digit, add a zero to the end of the dividend and keep going. Trailing zeros after a decimal point do not change its value, so 3 is the same as 3.000.
Example: 3 ÷ 8
3 ÷ 8 = 0.375, which is also the decimal for the fraction 3/8. The fraction to decimal calculator runs this same division for any fraction.
Dividing a decimal by a decimal
This is the case where moving the point matters. Count the decimal places in the divisor, then move both points that many places.
Example: 12.6 ÷ 0.42
0.42 has two decimal places, so move both points two places right. 12.6 has only one decimal digit, so add a zero to make room.
A quick estimate confirms it: 12 ÷ 0.4 is 120 ÷ 4 = 30.
Example: 15.3 ÷ 0.06
Example: 0.84 ÷ 0.07
The dividend can keep a decimal after the move; only the divisor has to be whole. 18.9 ÷ 2.7 becomes 189 ÷ 27 = 7, but 0.036 ÷ 1.2 becomes 0.36 ÷ 12 = 0.03, and you divide 0.36 by 12 just as in the previous section.
Dividing a whole number by a decimal
A whole number has an invisible decimal point at its end: 6 is 6.0, or 6.00. Write the point in, add zeros, and move it along with the divisor’s.
Example: 6 ÷ 0.25
In money terms: $6 is 24 quarters.
Example: 1.2 ÷ 0.005
Dividing by a number less than 1 always gives an answer bigger than the number you started with, because you are asking how many small pieces fit. The same thing happens in dividing fractions, and for the same reason: 0.25 is the fraction 1/4.
Dividing by common decimals
Some decimal divisors turn into simple multiplications. These are worth memorizing, especially for mental math with money.
| Dividing by | Same as | Example |
|---|---|---|
| 0.5 | × 2 | 2.75 ÷ 0.5 = 5.5 |
| 0.25 | × 4 | 5 ÷ 0.25 = 20 |
| 0.2 | × 5 | 8.4 ÷ 0.2 = 42 |
| 0.1 | × 10 | 45.6 ÷ 0.1 = 456 |
| 0.01 | × 100 | 5 ÷ 0.01 = 500 |
| 10 | move the point 1 place left | 45.6 ÷ 10 = 4.56 |
| 100 | move the point 2 places left | 45 ÷ 100 = 0.45 |
Each row works because dividing by a number is the same as multiplying by its reciprocal: the reciprocal of 0.25 (one quarter) is 4. Dividing by 10 or 100 slides every digit one or two places to the right in the place value chart, which looks like the decimal point moving left.
Repeating decimals and rounding the answer
Some divisions never finish. 2 ÷ 0.3 becomes 20 ÷ 3, and three goes into 20 six times with 2 left over, every time. The answer is 6.666…, with the 6 repeating forever.
When a remainder repeats, the digits repeat. Stop and round to the precision you need: 6.67 to two decimal places, or 6.7 to one. Say that the answer is rounded (≈ 6.67), so nobody mistakes it for exact. The guide to rounding to decimal places covers the rule, and the rounding calculator shows every place at once.
Example: price per pound
A 2.5 lb bag costs $7.47. What is the price per pound?
The unit price calculator does this comparison for up to four package sizes.
How to check your answer
Two quick checks catch nearly every misplaced decimal point.
- Estimate first. Round both numbers to something easy. For
12.6 ÷ 0.42, think 12 ÷ 0.4, which is 120 ÷ 4 = 30. If your answer were 3 or 300, you would know the point had slipped. - Multiply back. Quotient × divisor should equal the dividend:
30 × 0.42 = 12.6. The multiplication calculator handles the check when the numbers are long. - Bigger or smaller? Dividing by a number greater than 1 makes the answer smaller. Dividing by a number between 0 and 1 makes it bigger.
Common mistakes when dividing decimals
- Moving only one decimal point. Whatever you do to the divisor, do to the dividend. Moving just one changes the answer by a factor of 10, 100 or more.
- Moving the dividend’s point to make it whole. Only the divisor needs to become a whole number. The dividend moves the same number of places, wherever that leaves it.
- Forgetting to add zeros. In
6 ÷ 0.25, the 6 must become 600, not 6 or 60. - Misplacing the point in the answer. Write it above the dividend’s (moved) point before you start dividing, not at the end.
- Dropping a zero after the point.
0.036 ÷ 1.2is 0.03, not 0.3. Every place after the point needs a digit, even when it is 0. - Stopping too early. If there is a remainder, add zeros and continue, or round and say so.
Frequently asked questions
How do you divide decimals step by step?
Move the divisor’s decimal point right until it is a whole number, and move the dividend’s point the same number of places. Then divide as with whole numbers, placing the decimal point in the answer directly above the dividend’s point. For example, 4.5 ÷ 0.3 becomes 45 ÷ 3 = 15.
What is 6 divided by 0.25?
6 ÷ 0.25 = 24. Move both decimal points two places right to get 600 ÷ 25, which is 24. It makes sense with money: 0.25 is a quarter, and $6 is 24 quarters. Dividing by 0.25 is the same as multiplying by 4.
What is 4.5 divided by 0.3?
4.5 ÷ 0.3 = 15. The divisor has one decimal place, so move both points one place right: 45 ÷ 3 = 15. Check by multiplying back: 15 × 0.3 = 4.5. The answer is bigger than 4.5 because 0.3 is less than 1.
How do you divide a decimal by a whole number?
Divide exactly as you would with whole numbers, and put the decimal point in the answer directly above the decimal point in the dividend. For 9.36 ÷ 4, four goes into 9 twice, 13 three times and 16 four times, giving 2.34. If a remainder is left, add zeros and keep dividing.
Why do you move the decimal point when dividing decimals?
Moving both points the same number of places multiplies the dividend and divisor by the same power of 10, which leaves the answer unchanged, just as 1/2 equals 5/10. It turns the divisor into a whole number so you can use ordinary long division. Moving only one point would change the answer.
Why is the answer bigger when you divide by a decimal?
Dividing asks how many of the divisor fit into the dividend. When the divisor is less than 1, many of them fit, so the answer is larger than the number you started with: 6 ÷ 0.25 = 24 because 24 quarters make 6. Dividing by a number greater than 1 gives a smaller answer.
What do you do if the decimal answer keeps going?
If the same remainder keeps coming back, the digits repeat forever, as in 2 ÷ 0.3 = 20 ÷ 3 = 6.666…. Stop once you see the repeat and round to the precision you need, such as 6.67 to two decimal places. State that the answer is rounded by writing ≈ 6.67.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/how-to-divide-decimals/